A billiard ball is hit in an oblique fashion by the cue
and experiences a force P as shown in the figure (top view).
Consider the force P, the angle β,
the mass m, the radius r, and the polar mass moment of inertia
= 2/5 m r² of the billiard ball as given.
Write out the equations for the x- and y-component of the acceleration
of the center of mass due to force P.
- Write out the equation for the angular acceleration
of the ball due to force P.
- Use the results from (1) and (2) and the concept of relative acceleration
to derive the equation for the
point 1, the point at which P is hitting the ball assuming that at the
the angular velocity of the ball is still zero.